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The average of 10 numbers is 17. The first number is increased by 1, the second by 2 and so on such that the tenth number is increased by 10. What is the new average?
- a)22.5
- b)23.5
- c)22
- d)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The average of 10 numbers is 17. The first number is increased by 1, t...
The sum of the numbers will increase by 1 + 2 + 3 + 4 + . . . + 10 = 55
Thus, the average will increase by 55/10 = 5.5
Thus, the new average is 17 + 5.5 = 22.5
Hence, option 1.
Thus, the average will increase by 55/10 = 5.5
Thus, the new average is 17 + 5.5 = 22.5
Hence, option 1.
Most Upvoted Answer
The average of 10 numbers is 17. The first number is increased by 1, t...
Given:
- The average of 10 numbers is 17.
- The first number is increased by 1, the second by 2, and so on such that the tenth number is increased by 10.
To find:
- The new average of the 10 numbers after the increase.
Solution:
Let's assume the sum of the original 10 numbers is S.
The average of the original 10 numbers is given as 17. So, we have:
S/10 = 17
Now, let's calculate the sum of the new numbers after the increase.
The first number is increased by 1, so the new first number is (original first number + 1).
Similarly, the second number is increased by 2, so the new second number is (original second number + 2).
And so on, the tenth number is increased by 10, so the new tenth number is (original tenth number + 10).
The sum of the new numbers after the increase is given as:
(S + 1 + 2 + 3 + ... + 10)
The sum of the first 10 natural numbers can be calculated using the formula:
Sum = (n * (n + 1))/2
Using this formula, the sum of the new numbers after the increase is:
(S + (1 + 2 + 3 + ... + 10))
= (S + (10 * 11)/2)
= (S + 55)
Now, the number of terms in the new series is still 10, so the new average can be calculated as:
(S + 55)/10
Since we need to find the new average, we substitute the value of S from the given equation:
17 * 10 = S
S = 170
Substituting the value of S in the new average equation:
New Average = (170 + 55)/10
= 225/10
= 22.5
Hence, the new average of the 10 numbers after the increase is 22.5.
Therefore, the correct answer is option A) 22.5.
- The average of 10 numbers is 17.
- The first number is increased by 1, the second by 2, and so on such that the tenth number is increased by 10.
To find:
- The new average of the 10 numbers after the increase.
Solution:
Let's assume the sum of the original 10 numbers is S.
The average of the original 10 numbers is given as 17. So, we have:
S/10 = 17
Now, let's calculate the sum of the new numbers after the increase.
The first number is increased by 1, so the new first number is (original first number + 1).
Similarly, the second number is increased by 2, so the new second number is (original second number + 2).
And so on, the tenth number is increased by 10, so the new tenth number is (original tenth number + 10).
The sum of the new numbers after the increase is given as:
(S + 1 + 2 + 3 + ... + 10)
The sum of the first 10 natural numbers can be calculated using the formula:
Sum = (n * (n + 1))/2
Using this formula, the sum of the new numbers after the increase is:
(S + (1 + 2 + 3 + ... + 10))
= (S + (10 * 11)/2)
= (S + 55)
Now, the number of terms in the new series is still 10, so the new average can be calculated as:
(S + 55)/10
Since we need to find the new average, we substitute the value of S from the given equation:
17 * 10 = S
S = 170
Substituting the value of S in the new average equation:
New Average = (170 + 55)/10
= 225/10
= 22.5
Hence, the new average of the 10 numbers after the increase is 22.5.
Therefore, the correct answer is option A) 22.5.
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The average of 10 numbers is 17. The first number is increased by 1, the second by 2 and so on such that the tenth number is increased by 10. What is the new average?a)22.5b)23.5c)22d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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The average of 10 numbers is 17. The first number is increased by 1, the second by 2 and so on such that the tenth number is increased by 10. What is the new average?a)22.5b)23.5c)22d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The average of 10 numbers is 17. The first number is increased by 1, the second by 2 and so on such that the tenth number is increased by 10. What is the new average?a)22.5b)23.5c)22d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average of 10 numbers is 17. The first number is increased by 1, the second by 2 and so on such that the tenth number is increased by 10. What is the new average?a)22.5b)23.5c)22d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
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